US6606093B1 - Method and apparatus for antialiasing by gamma corrected area calculation - Google Patents
Method and apparatus for antialiasing by gamma corrected area calculation Download PDFInfo
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- US6606093B1 US6606093B1 US09/081,073 US8107398A US6606093B1 US 6606093 B1 US6606093 B1 US 6606093B1 US 8107398 A US8107398 A US 8107398A US 6606093 B1 US6606093 B1 US 6606093B1
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T11/00—2D [Two Dimensional] image generation
- G06T11/20—Drawing from basic elements, e.g. lines or circles
- G06T11/203—Drawing of straight lines or curves
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2200/00—Indexing scheme for image data processing or generation, in general
- G06T2200/12—Indexing scheme for image data processing or generation, in general involving antialiasing
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- the invention relates generally to display of video data in a computer system. More particularly, the invention relates to antialiasing of lines and/or points in a graphics display by gamma correction based on pixel area calculation.
- Graphical images are represented in typical computer systems by individual points on a computer monitor known as pixels. There are typically thousands or several million pixels in a single computer display that are individually manipulated to form the two-dimensional and three-dimensional images which a user sees on the computer screen.
- Each pixel is displayed at a specified intensity, with the intensity of each color component (e.g., red, green, and blue) pixel in a color system separately specified in accordance with the color model for the system.
- the pixel intensity is determined from the gray scale value of the pixel.
- video driver circuitry specifies a voltage for each pixel displayed (or color component pixel in the case of RGB color systems).
- Monitor response is nonlinear and a power law gamma correction curve describes the parametric relationship between the applied voltage (to the electron-gun or pixel driver) and the displayed pixel intensity.
- gamma correction of intensity The calculation by which the applied voltage needed to display a particular intensity is determined is known as gamma correction of intensity.
- the precise value of the gamma parameter is monitor dependent and typically varies from 2.0 to 3.0, although the National Television System Committee (NTSC) has defined a signal standard value of 2.2.
- the shape of the correction curve depends, in part, on the gamma parameter value.
- the driver voltages associated with predetermined pixel intensity values are stored in lookup tables, the number of entries in the lookup table ideally equaling the possible number of pixel intensity values.
- the table entry corresponding to that intensity level is looked up and the value therein applied to the driver circuitry.
- a line segment (which may be, but is not necessarily, a polygon boundary) has both length and width.
- Each line segment is bounded by two edges, the distance between the edges being the width of the line segment, and each edge is bounded by two endpoints, one at either end of each line segment edge.
- pixels are often thought of as points, each pixel has finite boundaries and a defined area.
- the pixel boundaries are the top, bottom, and sides of the pixel and the area is equal to the height times the width (i.e., length of a side boundary times the length of a top or bottom boundary). If the pixel dimensions are normalized, then each pixel boundary has a length of one and the magnitude of the area of each pixel is advantageously one.
- pixels in a computer graphics system are arranged in a rectangular grid, and are typically rectangular, purely vertical and horizontal lines (or line segments) and boundaries are generally displayed relatively precisely and with little distortion.
- lines that are not oriented at right angles are not neatly mapped onto adjacent pixels and undesirable distortions and artifacts can occur because of the imperfect mapping between diagonal lines and/or boundaries and pixels forming the display.
- the edges of lines and/or polygons often do not map to precisely defined locations on the pixel boundaries, such as when the edge is not parallel to a horizontal or vertical axis, which may further distort the displayed image.
- jaggies a form of distortion colloquially referred to as “jaggies” may occur because of the stair-stepping effect which can be seen when a diagonal line is represented by a series of diagonally adjacent pixels. This stair-stepping effect can be ameliorated by effectively blurring the pixels at the edge of a line.
- the present invention provides an improved technique for antialiasing by gamma correction of pixel intensity of covered pixels wherein the pre-gamma corrected intensity is relative to the amount of the pixel covered by a line as determined from the intersections of the edges of a line and pixel boundaries.
- line antialiasing is further enhanced by alpha-blending the line pixel with the background.
- the endpoints of antialiased line segments are evaluated appropriately by accurately assessing the amount of pixel area covered and varying the pixel intensity accordingly.
- FIG. 1A is an illustration of a diagonal line segment.
- FIG. 1B is an illustration of a pixel representation of a diagonal line segment.
- FIG. 1C is an illustration of a pixel representation of a wide line segment.
- FIG. 2 is an illustration of a line segment partially covering a plurality of pixels and triangles used to identify the point of interception between an edge of the line segment and a pixel boundary.
- FIG. 3 is a flowchart representation of a method of antialiasing in accordance with an embodiment of the present invention.
- FIG. 4 is a block diagram representation of a partial rasterizing engine illustrating elements used for antialiasing in accordance with an embodiment of the present invention.
- FIG. 5 is an illustration of a line segment and a quad of pixels.
- FIG. 6 is a block diagram of a line gamma correction block in a rasterizing engine in accordance with an embodiment of the present invention.
- Line antialiasing is desirable in a raster-scan computer graphics system where objects and lines are represented by a set of discrete points on horizontal scan lines on the screen.
- FIG. 1A a diagonal line 1 that is not pixelated is shown. Unlike a representation of the diagonal line on a computer display, the edges of the line are smooth and continuous, without any abrupt vertical or horizontal steps.
- FIG. 1B a 45° line on a pixelated display is shown. In contrast to the line of FIG. 1A, the line is represented by a series of rectangular non-adjacent pixels 2 - 8 .
- the two edges of the line are not smooth diagonal surfaces, rather they are formed by a series of horizontal and vertical pixel boundaries, creating an undesirable staircase effect.
- the staircase effect is shown on a relatively wide line 9 at an angle of approximately 30°. In a line that is more than one pixel wide, the pixels that are bounded by edge pixels and are inside the line are not antialiased.
- antialiasing is accomplished by varying the pixel intensity in relation to the amount of pixel area covered by the line segment.
- calculating the area of pixel coverage typically requires extensive computations, the present invention provides an improved technique by which the pixel coverage area may be computed using arithmetic, cross products and limited division.
- the gamma correction curve is characterized as a cubic spline and the desired output level is determined by linear interpolation applying the de Casteljau algorithm, eliminating the need for extensive storage and/or transfer of gamma correction curve tables.
- the pixel color attributable to the antialiased line segment is alpha blended with the background color where the degree of alpha blending is proportional to area of pixel coverage.
- Pixel 40 has four corners 41 , 42 , 43 and 44 ; and four boundaries corresponding to the sides of pixel 40 connecting the four corners (i.e., the four line segments from 41 to 42 , from 42 to 44 , from 41 to 43 , and from 43 to 44 ).
- each pixel intersected by an edge of the line segment is antialiased by changing the pixel intensity by an amount proportional to the area of the pixel covered by the line segment. Determination of the area of pixel coverage is a multiple step process which may be advantageously performed using line equations generated to draw the line segment and accordingly do not need to be computed separately solely for determination of pixel coverage.
- the area of the pixel covered by a line segment may be readily determined from the intersection points of the line segment edges and the pixel boundaries. These intersection points may, in turn, be advantageously determined from the triangles formed between the edges and each of the four pixel corners. Referring to FIG. 2, the edge 10 intersects a vertical boundary of pixel 40 at point 45 . All the corners of pixel 40 are known, including the lower left corner 41 and upper left corner 42 .
- the edge end points which are needed for the line equations defining the line segment edges irrespective of antialiasing, are made available to the antialiasing subsystem or algorithm as shown by input/output block 110 .
- the end points 11 and 12 of line segment edge 10 are therefore known.
- the area of a triangle formed by three known points can be readily determined using basic geometry, the areas of the eight triangles formed by the end points of the line segment edges 10 and 20 and the four corners of pixel 40 are readily calculated using addition, subtraction, multiplication and binary division.
- triangle 50 is formed by the end points 11 and 12 and pixel corner 41 .
- triangle 60 is formed by the endpoints 11 and 12 and pixel corner 42 .
- the location of the edge intercept 45 on the pixel boundary between pixel corners 41 and 42 is determined from the ratio of the triangle areas. This process is simultaneously or sequentially performed for each edge and each pixel boundary as indicated by processing block 120 of FIG. 3 .
- the three vertices of the triangle and the triangle ratio are also used to determine whether an edge intersects a pixel boundary and, if so, which of the pixel corners are inside the line segment (or polygon) of which the edge is a part.
- x ⁇ and y ⁇ are the x and y coordinates of vertices a, b, and c of the triangle.
- the distance from the edge to the pixel corner which is proportional to the triangle area, may be determined from the signed magnitude of the cross product as shown in equation 2 below
- x ⁇ and y ⁇ are the x and y coordinates of vertices a, b, and c of the triangle formed by the two endpoints of the edge and the pixel corner.
- the areas of triangles 50 and 60 have different signs.
- the sign of the triangle formed by the edge and the pixel corner indicates whether the pixel corner is covered by the line segment or lies outside of the line segment.
- triangles with vertices formed by covered pixel corners will have one sign and triangles with vertices formed by pixel corners that are not covered by the line segment will have the opposite sign.
- a four bit field is associated with each edge of a line segment and each bit of the field is associated with a pixel corner. As each triangle is evaluated, the bit associated with the corner forming a vertex of the triangle may be set (or cleared) to indicate that the pixel is covered. The four bit field can then be readily evaluated (by, for example, masking using logical AND operations) during pixel coverage evaluation.
- the ratio between the area of a first triangle formed by end points of an edge and a pixel corner and the result of the area of the first triangle less the area of a second triangle formed by the end points of the edge and the adjacent pixel corner on the same boundary is evaluated to determine whether the edge intersects the pixel boundary between the two pixel corners. If the ratio is not within the numeric range from zero to one, the edge does not intersect the pixel boundary between the two corners. If the ratio is greater than zero and less than one, then the edge intercepts the pixel boundary at the location indicated by the ratio. For example, if the ratio is 1 ⁇ 2, then the edge bisects the pixel boundary.
- the area bounded by each edge and the pixel boundary is determined using standard analytic geometry area calculations as shown in processing block 130 of FIG. 3 . If the edge crosses two adjacent pixel boundary edges and only one pixel corner is covered by the line segment, the covered pixel region is a triangle and the area is computed from the base and height of the covered triangle region wherein the base and height are determined from the intersection points. If the edge crosses two adjacent pixel boundary edges and three pixel corners are covered by the line segment, then the covered pixel region is equal to the total pixel area less the area of the triangle formed by the edge and the uncovered pixel corner.
- the area of this triangle is readily determined from the base and height of the covered triangle region wherein the base and height are determined from the intersection points. If the edge crosses two opposite edges of the pixel boundary, then the covered area is equal to the area of a rectangle with one dimension equal to the length of a pixel boundary and the second dimension equal to the average of the distances from the included pixel boundary to the two pixel boundary edge intersection points.
- the total pixel coverage is determined by summing the pixel coverage attributable to each edge and subtracting the area of a pixel from the sum as shown by processing block 140 of FIG. 3 .
- the pixel area is normalized, one is subtracted from the sum of the two pixel coverage areas attributable to each edge and the result is the total pixel area covered by the line segment.
- a line segment that is being evaluated for antialiasing that does not extend beyond the display boundaries will include endpoints within pixels.
- decision block 150 of FIG. 3 a determination is made as to whether the pixel includes an endpoint. If the pixel does include an endpoint, the pixel area determination is corrected to compensate for the reduced pixel coverage as shown by processing block 160 .
- the evaluated pixel coverage is treated as being linear across the pixel and is adjusted by a factor related to the actual end point location in the pixel.
- the calculated pixel coverage area is reduced in proportion to the extent to which the edge extends into the pixel. For example, if an edge ended in the middle of a pixel, the calculated pixel area coverage would be reduced by one half.
- the gamma-corrected coverage value is determined as shown by processing block 180 .
- the gamma corrected coverage value is determined from the gamma correction coefficients and the pixel coverage area.
- the gamma correction coefficients describe the gamma correction curve.
- the gamma correction coefficients are the control point coefficients of a cubic spline describing the gamma correction curve. Applying the de Casteljau algorithm, the point on the gamma correction curve corresponding to the desired pixel intensity as indicated by the pixel area coverage is determined by linear interpolation. This point on the gamma correction curve corresponds to the gamma corrected coverage value.
- the gamma corrected coverage value is used for alpha blending as shown by processing block 190 of FIG. 3 .
- Alpha blending is a technique for color blending that is particularly useful for rendering opaque surfaces.
- the antialiased line pixel color (source) is blended with the color of the pixel established by background objects (destination).
- the alpha blended color is defined as ⁇ S+(1 ⁇ )D where ⁇ is the gamma corrected coverage value, S is the source color (contributed by the antialiased line) and D is the pixel color before rendering the antialiased line.
- alpha blending is not used and the gamma corrected coverage value for each color component is applied directly to the display circuitry and the pixel (or sub-pixel) intensity corresponds directly to the gamma corrected coverage value.
- FIG. 4 A block diagram of a partial rasterizing engine illustrating elements used for antialiasing in accordance with an embodiment of the present invention is shown in FIG. 4 .
- the rasterizing engine receives instructions 210 (primarily graphical output primitives) from a transform engine (not shown).
- the received instructions are processed by parser 220 which transfers parsed instructions for drawing lines to line equation processor 230 .
- the line equation processor 230 generates the line equations used to draw lines on a display. These line equations are evaluated to generate raster lines on the display, including identification of pixels covered by each generated raster line.
- each pixel is evaluated to determine how much of the pixel area is covered by the line segment in line antialias block 240 .
- each edge is input to line antialias block 240 separately, and the input data include nine signed distances (one for each pixel corner in the quad) and an in sign status flag, indicating whether, relative to the edge being analyzed, a positive distance or a negative distance is in the line segment.
- the input data include nine signed distances (one for each pixel corner in the quad) and an in sign status flag, indicating whether, relative to the edge being analyzed, a positive distance or a negative distance is in the line segment. Referring to FIG. 5, a quad of four pixels, 281 , 282 , 283 , and 284 and a line segment with edges 291 and 292 are shown.
- Distance vectors 301 , 302 , 303 , 304 , 305 , 306 , 307 , 308 , and 309 from edge 291 to the nine corners of the quad are shown.
- Distance vectors 302 , 303 , 305 , 306 , 308 and 309 have the same sign and this sign is the in sign.
- Distance vectors 301 , 304 , and 307 have the opposite sign.
- the signed distances are the signed magnitudes of the cross products of the edge end points and the pixel corners as defined in equation 2 above.
- only four signed distances (and an in sign flag) would be input to the line antialias block 240 for each edge.
- the line antialias block outputs an endpoint corrected pixel area coverage value 245 for each pixel.
- the endpoint corrected pixel area coverage values are input into line gamma correction block 250 .
- the line gamma correction block 250 also receives programmable coefficients 260 as inputs.
- the programmable coefficients are cubic spline control points describing the gamma correction curve for the display associated with the computer graphics system.
- the cubic spline approximation of the gamma correction curve is a Bézier curve.
- the line gamma correction block implements the de Casteljau algorithm in which the point on a Bézier curve with a specified parameter may be determined by successive linear interpolations.
- the parameter is the endpoint corrected pixel area coverage value 245 and the Bézier curve is an approximation of the gamma correction curve.
- four Bézier curve control points, 261 , 262 , 263 , and 264 are input into three linear interpolation blocks 271 , 272 , and 273 of line gamma correction block 250 .
- the endpoint corrected pixel area coverage value 245 is the interpolation coefficient input into each of the linear interpolation blocks 271 , 272 , and 273 .
- the linear interpolation block 271 outputs an interpolated result between control points 261 and 262 which is input to linear interpolation block 274 .
- linear interpolation block 272 outputs an interpolated result between control points 262 and 263 which is input into linear interpolation blocks 274 and 275 and linear interpolation block 273 outputs an interpolated result between control points 263 and 264 which is input into linear interpolation block 275 .
- Linear interpolation blocks 274 and 275 also receive an interpolation coefficient from endpoint corrected pixel area coverage value 245 and each output a result interpolated between their respective inputs.
- linear interpolation blocks 274 and 275 are input into linear interpolation block 276 which similarly receives an interpolation coefficient input of the endpoint corrected pixel area coverage value 245 and outputs a gamma corrected coverage value 270 which corresponds to the point on the gamma correction curve for the desired pixel (or sub pixel) intensity.
- the gamma corrected coverage value 270 may be used as an input for alpha blending as described above or, alternatively, stored directly in a frame buffer.
- a method and apparatus for antialiasing by gamma corrected pixel area calculation is disclosed in which pixel area coverage is advantageously computed without supersampling or requiring extensive computations that are difficult to efficiently implement in a computer system and gamma correction is readily and flexibly implemented without requiring unwieldy table operations.
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